Three-dimensional shapes
A box, a can, a ball and a pyramid all take up room. What tells them apart, and what words describe a solid to someone who cannot see it?
Where you are 7 inside
What this area is about
A solid takes up space: it can be picked up, turned over and seen from every side. Solids split into two kinds, those made only of flat polygons and those with a curved surface, and each kind has a few families worth naming part by part.
How these fit together
First words. Naming and describing solid shapes tells a cube, sphere, cone and cylinder apart, and faces, edges and vertices names the parts: flat surfaces, the lines where two faces meet, the corners where edges meet.
Flat-sided solids. Polyhedra are solids whose faces are all polygons; for every polyhedron without a hole through it, F + V - E = 2. Prisms and pyramids are the two families met most: two congruent bases in parallel planes, or one base and an apex. The five regular solids answer a sharper question: a convex polyhedron with congruent regular faces and the same number meeting at every vertex comes in exactly five kinds.
Curved solids. Cylinders and cones are built on circles, and a sphere is every point in space at one distance r from a center.
A path through it
Naming solid shapes comes first. Faces, edges and vertices and polyhedra both follow it, and prisms and pyramids and the five regular solids both come after polyhedra. Cylinders, cones and spheres need only what a circle is, so they fit anywhere.
After this come nets, cross sections, volume of prisms and cylinders and surface area of a sphere.